1. Field of the Invention
The present invention relates to an optical fiber suitable as an optical transmission path, a dispersion compensator, an optical filter, an optical power equalizer and an optical amplifier.
2. Description of the Related Art
Conventionally, optical fibers composed of alternately arranged annular layers of high and low refractive indices have been known and disclosed in J. Marcou, et al., xe2x80x9cMonomode photonic band gap fibers for dispersion shifting towards short wavelengthsxe2x80x9d ECOC""99, I-pp.24-25 (hereinafter called D1) and Y. Fink, et al., xe2x80x9cGuiding optical light in air using an all-dielectric structurexe2x80x9d Journal of Lightwave Technology, vol.17, No.11, November, 1999 pp, 2039-2041 (hereinafter called D2).
In these optical fibers, light is confined in the center region, which is called the core region, surrounded by annular layers, which is called the cladding region. The refractive index of the core region is lower than the refractive indices of the annular layers in the cladding region. Accordingly, the confinement of light in the core is not based on total internal reflection but on Bragg reflection due to the regularity in the radial profile of refractive index. That is, a diverging cylindrical wave centered at the fiber axis is strongly coupled to a converging cylindrical wave centered at the fiber axis because of the regularity in the radial profile of refractive index in the cladding region. As a result, the diverging cylindrical wave is reflected by the annular layers in the cladding, and is confined in the core.
The thicknesses of the annular layers in the cladding are not necessarily uniform. In D1, the refractive index distribution is designed to have the periodicity based on the Bessel functions, while in the D2, the thicknesses of the layers are determined in accordance with the zero points of the Bessel functions.
Further, in R. F. Cregan, et al xe2x80x9cSingle-Mode photonic band gap guidance of light in airxe2x80x9d, Science, vol.285, pp.1537-1539 (September, 1999)(hereinafter called D3), an optical fiber having a cross-sectional structure in which a defect is introduced in a refractive index periodic structure having a two-dimensional translational symmetry is disclosed. In the cross section of this optical fiber, small regions (cells) having given refractive index distribution are regularly arranged, and some of the cells are replaced with cells having different refractive index distribution, resulting in breaking of the translational symmetry of the cross-sectional refractive index distribution. Those symmetry-breaking cells are called defects.
The two-dimensional periodic structure of the refractive index, if properly designed, reflects light belonging to a given wavelength band regardless of angle of incidence. Such a wavelength band is called a full PBG (full Photonic Band Gap). The light having the wavelength within the PBG is confined in the defect in the periodic structure. The periodic structure and the defect extend along the fiber axis and hence, the light propagates along the fiber axis.
Further, U.S. Pat. No. 5,802,236 discloses an optical fiber which includes a core and a cladding, wherein the effective refractive index of the core is higher than the effective refractive index of the cladding and the cladding has cladding feature structures which are arranged non-periodically. In such an optical structure, since the effective refractive index of the core is higher than the effective refractive index of the cladding, the light is confined in the core by total internal reflection. Here, assuming that a non-uniform region having spatially varying refractive index can be replaced with a homogeneous medium with maintaining the same optical characteristics, the effective refractive index is defined as the refractive index of such a homogeneous medium.
It is also conventionally known that Bragg reflection mirror can be formed by regularly laminating planar thin films consisting of media having different refractive indices, and that a high reflection efficiency is achieved by meeting the quarter wavelength condition where the optical thicknesses of the thin films are equal to a quarter wavelength.
However, in the optical fiber disclosed in D1, the refractive index difference between neighboring two annular layers is small (relative refractive index difference being 0.5%) because it is formed by doping Ge into silica glass.
Accordingly, the reflection efficiency of the annular layers in the cladding becomes small, and hence optical confinement to the core becomes weak. As a result, the optical power leaks to the outside of the fiber so that the transmission loss, particularly the transmission loss due to the bending of the fiber, increases.
On the other hand, in the optical fiber described in D2, the cladding region is composed of tellurium (refractive index being 4.6) and polystyrene (refractive index being 1.59). Due to the large difference in refractive index between the media, a high reflection efficiency can be obtained. However, the fabrication of this optical fiber is difficult for the following reason. According to the fabrication method disclosed in D2, this optical fiber is obtained by alternately depositing a tellurium film having a thickness of approximately 0.8 xcexcm and a polystyrene film having a thickness of approximately 1.6 xcexcm on an outer periphery of a glass tube of a diameter of 1.92 mm. However, it is difficult to fabricate a long fiber uniformly by this method. This is because if the optical fiber is wound in a coil while the films are deposited on it, it is difficult to deposit the films with uniform thickness. On the other hand, if the fiber is not wound in a coil shape, it is difficult to fabricate a long fiber because the length is limited by the size of the depositing facility. For example, the fiber length which is reported in the above-mentioned literature is as short as 10 cm. Further, since the films are deposited on a cylindrical surface, the control of the film thickness is difficult compared with the conventional thin film forming where the films are deposited on a planar surface. This also makes it difficult to fabricate a fiber which is uniform along its axis.
Further, in the optical fiber described in D3, the size of the defect is limited to integer times of the size of the cells of the periodic structure in the cross-sectional refractive index distribution. Accordingly, the size of the core is also limited to integer times of the size of the cells. The diameter of the core affects the number of guided modes and the degree of the optical confinement of the guided modes. Accordingly, the limited range of selection of the core diameter results in the limited range of achievable optical characteristics of the optical fiber. Particularly, it becomes difficult to deliberately control the wavelength range for single-mode operation and the tolerance to bending.
The present invention has been made in view of the above and it is an object of the present invention to provide an optical fiber based on confinement by Bragg reflection which exhibits strong optical confinement to the core, facilitates the fabrication of a long fiber, and realizes a high freedom in selection of the core diameter.
To achieve such an object, the optical fiber according to the present invention is the optical fiber consisting of a core region and a cladding region which surrounds the core region and has a plurality of regions spaced apart in cross section and made of sub mediums, whose refractive indices differ from that of a main medium constituting the cladding region, wherein the core region has lower mean refractive index than that of the cladding region, and wherein the arrangement of the regions made of sub mediums has such a regularity in the radial direction of the optical fiber that the light with given wavelength, propagation coefficient and electric field distribution propagates along the fiber axis and has not less than 50% of its total propagating power in the core region, and the arrangement does not have translational symmetry in cross section.
The main medium is a medium which can practicably constitute the optical fiber by itself and the main medium region must not be divided in a single optical fiber. On the other hand, the sub medium may be a medium which cannot constitute the optical fiber by itself. For example, the main medium may be silica glass and the sub medium may be gas or may be evacuated.
The mean refractive index navg of a given circular annular region is defined by the following equation                               n          avg                =                                            1                              π                ⁡                                  (                                                            b                      2                                        -                                          a                      2                                                        )                                                      ⁢                                          ∫                a                b                            ⁢                              ∮                                                                            n                      2                                        ⁡                                          (                                              r                        ,                        θ                                            )                                                        ⁢                                      ⅆ                    θ                                    ⁢                                      xe2x80x83                                    ⁢                  r                  ⁢                                      xe2x80x83                                    ⁢                                      ⅆ                    r                                                                                                          (1)            
where xe2x80x9caxe2x80x9d and xe2x80x9cbxe2x80x9d are respectively the inner radius and the outer radius of the circular annular region, and r and xcex8 are polar coordinates in the cross section and n (r, xcex8) is a function giving the refractive index at the position (r, xcex8). 
According to the present invention, by arranging the sub mediums with a regularity in the radial direction of the fiber, it becomes possible to regularly change the mean refractive index in the radial direction in the cladding region. Eventually, it becomes possible to confine the light in the core by Bragg reflection. Moreover the use of the sub medium enables grater change in the mean refractive index than the conventional doped-glass technique and can realize stronger optical confinement to the core than the conventional technique.
Further, since the arrangement of the sub mediums does not have translational symmetry, the core diameter is not limited to integer times of the cell size. The great freedom in selecting the core diameter makes it possible to optimize the number of guided modes and the strength of the optical confinement of guided mode.
The translational symmetry of an arrangement is a property that the arrangement stays substantially unvaried when it is moved in a given direction by a given distance. Here, the vector specifying the direction and the distance of such movement operation is called a lattice vector. Further, the two-dimensional translational symmetry of an arrangement is a property that the arrangement has two independent lattice vectors.
It is preferable that the regions made of sub mediums are substantially arranged on one or more concentric circumferences centered at the fiber axis in the cross section of the fiber. Due to such a constitution, the mean refractive index of an annular region containing one of the circumferences on which the sub mediums are arranged can be made greatly different from that of the neighboring annular regions, and hence strong optical confinement can be realized.
Alternately, it is preferable that the cladding region consists of a plurality of concentric cylindrical regions, where regions having high and low mean refractive indices are arranged alternately in the radial direction.
In this manner, by alternating the high mean refractive index regions and the low mean refractive index regions, a mode coupling is generated between cylindrical lightwaves propagating outward and inward so that it becomes possible to reflect the cylindrical lightwave propagating outward efficiently and confine it to the core region.
It is preferable that respective optical thicknesses of respective cylindrical regions effectively equal to the quarter wavelength of the given mode optical wave. Here, xe2x80x9coptical thicknesses effectively equal to the quarter wavelengthxe2x80x9d means a condition where the diagonal components of the characteristic matrix Mi expressed below become substantially zero.   Mi  =            [              xe2x80x83            ⁢                                                  m              11                                                          m              12                                                                          m              21                                                          m              22                                          ⁢              xe2x80x83            ]        =                                        πκ            i                    ⁢                                                    a                                  i                  -                  1                                            ⁢                              a                i                                                              -          2                    xc3x97              [                  xe2x80x83                ⁢                                                                                                                        J                      v                                        ⁡                                          (                                              i                        -                        1                                            )                                                        ⁢                                                            N                                              v                        +                        1                                                              ⁡                                          (                      i                      )                                                                      -                                                                            J                                              v                        +                        1                                                              ⁡                                          (                      i                      )                                                        ⁢                                                            N                      v                                        ⁡                                          (                                              i                        -                        1                                            )                                                                                                                                            -                                      η                    i                                          -                      1                                                                      ⁢                                  {                                                                                                              J                          v                                                ⁡                                                  (                                                      i                            -                            1                                                    )                                                                    ⁢                                                                        N                          v                                                ⁡                                                  (                          i                          )                                                                                      -                                                                                            J                          v                                                ⁡                                                  (                          i                          )                                                                    ⁢                                                                        N                          v                                                ⁡                                                  (                                                      i                            -                            1                                                    )                                                                                                      }                                                                                                                          η                  i                                ⁢                                  {                                                                                                              J                                                      v                            +                            1                                                                          ⁡                                                  (                                                      i                            -                            1                                                    )                                                                    ⁢                                                                        N                                                      v                            +                            1                                                                          ⁡                                                  (                          i                          )                                                                                      -                                                                                            J                                                      v                            +                            1                                                                          ⁡                                                  (                          i                          )                                                                    ⁢                                                                        N                                                      v                            +                            1                                                                          ⁡                                                  (                                                      i                            -                            1                                                    )                                                                                                      }                                                                                                                                                J                      v                                        ⁡                                          (                      i                      )                                                        ⁢                                                            N                                              v                        +                        1                                                              ⁡                                          (                                              i                        -                        1                                            )                                                                      -                                                                            J                                              v                        +                        1                                                              ⁡                                          (                                              i                        -                        1                                            )                                                        ⁢                                                            N                      v                                        ⁡                                          (                      i                      )                                                                                                          ⁢                  xe2x80x83                ]            
where, aixe2x88x921 is the inner radius of the i-th cylindrical region, ai is the outer radius of the i-th cylindrical region and xcexai is the propagation constant in the radial direction in the i-th cylindrical region which is defined as follows.
xcexai={square root over (ni2k02xe2x88x92xcex22)}
where, ni is the refractive index of the i-th cylindrical region, k0 is the wave number in vacuum, and xcex2 is the a propagation constant in the axial direction. Further, xcex7i is the effective refractive index of the i-th cylindrical region, wherein
xcex7i=xe2x88x92k0/xcexai for TE mode
xcex7i=k0ni2/xcexai for TM mode
xcex7i≈xe2x88x92xcexai/xcex2 for LP01 mode
Further, Jv and Nv are the first-kind and second-kind Bessel functions of the v-th order respectively. Also, Jv(xcexaiai) is expressed as Jv(i), Nv(xcexaiai) is expressed as Nv(i), Jv(xcexaiaixe2x88x921) is expressed as Jv(ixe2x88x921) and Nv(xcexaiaixe2x88x921) is expressed as Nv(ixe2x88x921).
Although, it is in some cases difficult to make both of the diagonal components of Mi exactly equal to zero, the inventors have found out that it is sufficient for tight confinement of light to the core to make the diagonal components m11 and m22substantially equal to zero alternately, that is, to make m11 substantially equal zero in the i-th region, m22substantially equal to zero in the (i+1)-th region, and so forth. Such a condition to achieve high reflectivity in the cladding and tight confinement of light to the core is called a pseudo quarter wavelength condition.
By forming the core region by a void or silica glass, the transmission loss can be reduced. Further, by making the core of an optical gain medium, an optical amplifier having the gain characteristics with small dependency on wavelength can be realized. In a constitution where the core region is composed of an inner core region and an outer core region which surrounds the inner core region and has the refractive index lower than the refractive index of the inner core region, it becomes possible to reduce the bending loss in the basic mode without deteriorating the cut-off characteristics of higher order modes.
This optical fiber can be suitably used as a band-pass optical filter and a gain equalizer. Also, an optical transmission path can be constituted by such an optical fiber and another optical fiber whose dispersion is of the opposite sign to that of such an optical fiber.